A man attaches the Kurdish flag a bus that will transport Syrian refugees from Kobani to the Basirma refugee camp in Iraqi Kurdistan.
Photograph: Bram Janssen/AP

Turkey would not agree to any US arms transfers to Kurdish fighters who are battling Islamic State (Isis) militants in Syria, President Recep Tayyip Erdogan was quoted as saying on Sunday, as the extremist group fired more mortar rounds near the Syrian-Turkish border and fighting around the besieged town of Kobani intensified.

Turkey views the main Syrian Kurdish group, the PYD, and its military wing which is fighting Isis militants as an extension of the PKK, which has waged a 30-year insurgency in Turkey and is designated a terror group by the US and Nato.

Washington has said recently that it has engaged in intelligence sharing with Kurdish fighters and officials have not ruled out future arms transfers to the Kurdish fighters.

“The PYD is for us, equal to the PKK. It is a terror organisation,” Erdogan told a group of reporters on his return from a visit to Afghanistan. “It would be wrong for the United States with whom we are friends and allies in Nato to talk openly and to expect us to say ‘yes’ to such a support to a terrorist organisation.”

Erdogan’s comments were reported by the state-run Anadolu agency on Sunday.

In Washington, the Texas senator Ted Cruz, a presumed candidate for the Republican presidential nomination in 2016, criticised President Barack Obama for not aiding the Kurdish fighters.

“We have dropped a bomb here and a missile there, but it has been a photo-op foreign policy,” Cruz said.

Turkey’s opposition to arms transfers to the Kurdish forces, meanwhile, is hampering the US-led coalition’s efforts to fight the extremists and further complicating relations between Turkey and Washington. The countries are involved in negotiations about Ankara’s role with the US and Nato allies fighting the Islamic State group, which is attempting to capture Kobani.

Turkey has demanded that the coalition widen its campaign against the militants by providing greater aid to Syrian rebels, who are battling both Isis and President Bashar al-Assad’s forces. Turkey has so far provided sanctuary to an estimated 200,000 Syrians fleeing Kobani, and recently agreed to train and equip moderate Syrian rebel fighters trying to remove Assad from power.

The White House said President Barack Obama spoke to Erdogan on Saturday about the situation in Kobani and steps that could be taken to counter Isis advances.

“The two leaders pledged to continue to work closely together to strengthen cooperation against [Isis],” a statement said.

Fighting between the militants and the Kurdish fighters defending Kobani continued on Sunday. Mortar strikes hit the town, sending plumes of smoke into the air. Three mortars also fell on the Turkish side of the border, landing in an open field where they caused no injuries. On Saturday and Sunday, Isis appeared to be targeting the border crossing area, potentially in a bid to hamper Kobani’s last link to the outside world.

Thick smoke and flames from a fire rises following a strike in Kobani. Photograph: Lefteris Pitarakis/AP

In an attempt to stave off the advance, a US-led coalition has been carrying out air strikes on Isis positions in and near the town, as well as in other parts of Syria, particularly in the oil-rich eastern province of Deir el-Zour, as well as in Iraq. Several air strikes hit Kobani on Saturday evening. US-led warplanes launched 11 air strikes near Kobani on Saturday and Sunday, US Central Command said.

The flow of migrants into Turkey has intensified since Isis’s push to take Kobani and cut access for Kurdish fighters to other areas of Syria they control. On Saturday, Isis fighters also weighed in on their attempts to take Kobani, arguing it was not a fight against the Kurds.

“We came to establish the laws of God not to fight the Kurds,” a fighter in army fatigues said on a video uploaded to YouTube. The video was uploaded by a user who appears to be embedded with the militants in Kobani. It appeared genuine and reflected Associated Press reporting.

But another fighter who appeared to be from a European country, judging from his accent in Arabic, described their aim “to liberate the land from the fifth of the apostates, the PKK and others”, referring to Kurdish secular fighters who are overwhelmingly Sunni Muslim as apostates.

The fighter said the US-led coalition to fight the militant group was a sure sign of the justness of their cause.

“As for the planes that shell us 24 hours, day and night, by God we say: they increase our faith, assuredness and steadfastness. We know we are on the right path because all the [non-believers] of the world have gathered against us.”

The United Nations humanitarian chief, Valerie Amos, visited one of the refugee camps set up in a school in the Turkish border town of Suruc. While 900,000 people have been registered as refugees in Turkey since the Syrian crisis began four years ago, “the reality is that the numbers are nearer to 1.6 million”, Amos said.

“Of course countries have concerns about security, and about the impact on their economies and on essential services like health and education. But it’s also a crisis with a huge human impact,” she said.

“The international community has to continue to do all it can to find a political solution to this crisis.”